All-cis helical polypeptides

The possibility of all-cis open-chain polypeptides is rarely addressed, owing to three main reasons, namely, (i) the extreme scarcity of cis peptide bonds in naturally occurring proteins and peptides, (ii) the lesser thermodynamic stability (by about 2.5 kcal/mol) of cis amide bonds with respect to their trans counterparts, and (iii) widely held preconceptions about the so-called "steric clash" between lateral chains borne by two successive alpha carbons. Quantum-chemistry calculations performed on alanine tridecamers show how the latter constraints can be efficiently relieved through proper phi/psi adjustments along the backbone, leading to several helical arrangements--presumably the only permitted regular structures. Four more-or-less regular helices were thus characterized, one of them, a superhelix, exhibiting intramolecular hydrogen bonds. Understanding and anticipating all-cis open-chain structures not only make use of the classical Ramachandran maps at each C alpha i, relating to E = f(phi i,psi i), but also require the profile of a new kind of conformational dependence, the plaque maps, relating to E = f(phi i,psi i-1). The obvious coupling between two such maps enforces conformational dependence between two consecutive C alpha's, somewhat questioning in this context the customary "local effects", and presumably reducing the whole chain plasticity. Whereas cis thermodynamic penalty cannot be abolished locally, energy clues indicate that assembling cis-prepared building units is an exothermic process. Besides, once built up, the all-cis backbone should be difficult to unlock, thus affording reasonable kinetic stability.     

Dihedral angles of trialanine in D2O determined by combining FTIR and polarized visible Raman spectroscopy

We have measured the polarized visible Raman and FTIR spectra of trialanine and triglycine in D(2)O at acid, neutral, and alkaline pD. From the Raman spectra we obtained the isotropic and the anisotropic scattering. A self-consistent spectral analysis of the region between 1550 and 1800 cm(-1) was carried out to obtain the intensities, frequencies, and halfwidths of the respective amide I bands. A model was developed by means of which the intensity ratios of the amide I bands in all spectra and the respective frequency differences were utilized to determine the orientational angle theta between the peptide groups and the strength of excitonic coupling between the corresponding amide I modes. By exploiting results from a recent ab initio study on triglycine (Torii, H; Tasumi, M. J. Raman Spectrosc. 1998, 29, 81), we used these parameters to determine the dihedral angles phi and psi between the peptide groups. Our results show that trialanine adopts a 3(1)-helical structure in D(2)O for all of its three protonation states. The structure is insensitive to the carboxylate protonation and changes only slightly with N-terminal protonation. Triglycine is structurally more heterogeneous in the zwitterionic and the cationic state. Our spectral analysis suggests that 3(1)-helices coexist with right-handed alpha-helical and/or with beta-turn conformations. The N-terminal protonation stabilizes the 3(1)-structure. Our study provides compelling evidence that tripeptides adopt stable conformations in aqueous solution and that they are suitable model systems to investigate the initiation of secondary structure formation.     

The relationship between peptide plane rotation (PPR) and similar conformations

Currently, several energy functions and conformational search methods have been developed that are based on the observed distribution of phi and psi angles in protein structures. The definition of phi and psi angles is directly related to the orientation of the peptide plane (CA CO NH CA). Starting from one conformation and rotating a single peptide plane, the angles psi for one residue and phi for the consecutive residue that are linked by the peptide plane, display a continuous range of values within one global conformation. When peptide plane rotation is analyzed in several different conformations generated from a restricted conformation database, a large number of these conformations are related. Based on these observations, a new simplified all-atom representation for protein folding simulations is presented where only one torsion angle variable is required for each residue. The underlying theme of this article is that conformational search methods using phi and psi torsion space, search through many redundant conformations. These conformations are related by anticorrelated torsion changes of peptide plane rotations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 947–955, 1999     

Determination of conformational preferences of dipeptides using vibrational spectroscopy

The NMR coupling constants ((3)J(H(N), H(alpha))) of dipeptides indicate that the backbone conformational preferences vary strikingly among dipeptides. These preferences are similar to those of residues in small peptides, denatured proteins, and the coil regions of native proteins. Detailed characterization of the conformational preferences of dipeptides is therefore of fundamental importance for understanding protein structure and folding. Here, we studied the conformational preferences of 13 dipeptides using infrared and Raman spectroscopy. The main advantage of vibrational spectroscopy over NMR spectroscopy is in its much shorter time scale, which enables the determination of the conformational preferences of short-lived states. Accuracy of structure determination using vibrational spectroscopy depends critically on identification of the vibrational parameters that are sensitive to changes in conformation. We show that the frequencies of the amide I band and the A12 ratio of the amide I components of dipeptides correlate with the (3)J(H(N), H(alpha)). These two infrared vibrational parameters are thus analogous to (3)J(H(N), H(alpha)), indicators for the preference for the dihedral angle phi. We also show that the intensities of the components of the amide III bands in infrared spectra and the intensities of the skeletal vibrations in Raman spectra are indicators of populations of the P(II), beta, and alpha(R) conformations. The results show that alanine dipeptide adopts predominantly a PII conformation. The population of the beta conformation increases in valine dipeptides. The populations of the alpha(R) conformation are generally small. These data are in accord with the electrostatic screening model of conformational preferences.     

Extending the treatment of backbone energetics in protein force fields: limitations of gas-phase quantum mechanics in reproducing protein conformational distributions in molecular dynamics simulations

Computational studies of proteins based on empirical force fields represent a powerful tool to obtain structure-function relationships at an atomic level, and are central in current efforts to solve the protein folding problem. The results from studies applying these tools are, however, dependent on the quality of the force fields used. In particular, accurate treatment of the peptide backbone is crucial to achieve representative conformational distributions in simulation studies. To improve the treatment of the peptide backbone, quantum mechanical (QM) and molecular mechanical (MM) calculations were undertaken on the alanine, glycine, and proline dipeptides, and the results from these calculations were combined with molecular dynamics (MD) simulations of proteins in crystal and aqueous environments. QM potential energy maps of the alanine and glycine dipeptides at the LMP2/cc-pVxZ//MP2/6-31G* levels, where x = D, T, and Q, were determined, and are compared to available QM studies on these molecules. The LMP2/cc-pVQZ//MP2/6-31G* energy surfaces for all three dipeptides were then used to improve the MM treatment of the dipeptides. These improvements included additional parameter optimization via Monte Carlo simulated annealing and extension of the potential energy function to contain peptide backbone phi, psi dihedral crossterms or a phi, psi grid-based energy correction term. Simultaneously, MD simulations of up to seven proteins in their crystalline environments were used to validate the force field enhancements. Comparison with QM and crystallographic data showed that an additional optimization of the phi, psi dihedral parameters along with the grid-based energy correction were required to yield significant improvements over the CHARMM22 force field. However, systematic deviations in the treatment of phi and psi in the helical and sheet regions were evident. Accordingly, empirical adjustments were made to the grid-based energy correction for alanine and glycine to account for these systematic differences. These adjustments lead to greater deviations from QM data for the two dipeptides but also yielded improved agreement with experimental crystallographic data. These improvements enhance the quality of the CHARMM force field in treating proteins. This extension of the potential energy function is anticipated to facilitate improved treatment of biological macromolecules via MM approaches in general.     

Solvent and conformation dependence of amide I vibrations in peptides and proteins containing proline

We present a mixed quantum-classical model for studying the amide I vibrational dynamics (predominantly CO stretching) in peptides and proteins containing proline. There are existing models developed for determining frequencies of and couplings between the secondary amide units. However, these are not applicable to proline because this amino acid has a tertiary amide unit. Therefore, a new parametrization is required for infrared-spectroscopic studies of proteins that contain proline, such as collagen, the most abundant protein in humans and animals. Here, we construct the electrostatic and dihedral maps accounting for solvent and conformation effects on frequency and coupling for the proline unit. We examine the quality and the applicability of these maps by carrying out spectral simulations of a number of peptides with proline in D(2)O and compare with experimental observations.     

Simulation of infrared spectra for beta-hairpin peptides stabilized by an Aib-Gly turn sequence: correlation between conformational fluctuation and vibrational coupling

Vibrational spectra of a 12-residue beta-hairpin peptide, RYVEVBGKKILQ (HBG), stabilized by an Aib-Gly turn sequence (B = Aib) were investigated theoretically using a combination of molecular dynamics (MD) and density functional theory (DFT) calculations. Selected conformations of HBG were extracted from a classical MD trajectory and used for spectral simulations. DFT calculations, based on the Cartesian coordinate spectral property transfer protocol, were carried out for peptide structures in which all residues are replaced with Ala, except for the Aib and Gly residues, but the backbone (phi, psi, omega) structure of the original configuration is retained. The simulations provide a basis for interpretation of the HBG amide I infrared spectra in terms of structural variables such as detailed secondary structure and thermal conformational fluctuation as well as vibrational coupling as indicated by spectra of 13C isotope-labeled variants. The characteristic amide I band shape of such small beta-hairpin peptides appears to arise from the structure of the short antiparallel beta-sheet strands. The role of structural parameter fluctuation in vibrational coupling is evaluated by comparison of DFT-derived amide coupling constants for selected configurations and from transition dipole coupling calculations of coupling parameters between (13)C isotopically labeled residues for a MD-derived ensemble of configurations. Calculated results were compared with the experimentally obtained spectra for several (13)C isotope-labeled peptides of this sequence.     

Peptide bond vibrational coupling

Neutral trialanine (Ala3), which is geometrically constrained to have its peptide bond at Phi and Psi angles of alpha-helix and PPII-like conformers, are studied at the B3LYP/6-31+G(d,p) level of theory to examine vibrational interactions between adjacent peptide units. Delocalization of the amide I, amide II, and amide III3 vibrations are analyzed by calculating their potential energy distributions (PED). The vibrational coupling strengths are estimated from the frequency shifts between the amide vibrations of Ala3 and the local amide bond vibrations of isotopically substituted Ala3 derivatives. Our calculations show the absence of vibrational coupling of the amide I and amide II bands in the PPII conformations. In contrast, the alpha-helical conformation shows strong coupling between the amide I vibrations due to the favorable orientation of the C=O bonds and the strong transitional dipole coupling. The amide III3 vibration shows weak coupling in both the alpha-helix and PPII conformations; this band can be treated as a local independent vibration. Our calculated results in general agree with our previous experimental UV Raman studies of a 21-residue mainly alanine-based peptide (AP).     

Ramachandran-type plots for glycosidic linkages: Examples from molecular dynamic simulations using the Glycam06 force field

The goals of this article are to (1) provide further validation of the Glycam06 force field, specifically for its use in implicit solvent molecular dynamic (MD) simulations, and (2) to present the extension of G.N. Ramachandran's idea of plotting amino acid phi and psi angles to the glycosidic phi, psi, and omega angles formed between carbohydrates. As in traditional Ramachandran plots, these carbohydrate Ramachandran-type (carb-Rama) plots reveal the coupling between the glycosidic angles by displaying the allowed and disallowed conformational space. Considering two-bond glycosidic linkages, there are 18 possible conformational regions that can be defined by (alpha, phi, psi) and (beta, phi, psi), whereas for three-bond linkages, there are 54 possible regions that can be defined by (alpha, phi, psi, omega) and (beta, phi, psi, omega). Illustrating these ideas are molecular dynamic simulations on an implicitly hydrated oligosaccharide (700 ns) and its eight constituent disaccharides (50 ns/disaccharide). For each linkage, we compare and contrast the oligosaccharide and respective disaccharide carb-Rama plots, validate the simulations and the Glycam06 force field through comparison to experimental data, and discuss the general trends observed in the plots.     

Dihedral psi angle dependence of the amide III vibration: a uniquely sensitive UV resonance Raman secondary structural probe.

UV resonance Raman studies of peptide and protein secondary structure demonstrate an extraordinary sensitivity of the amide III (Am III) vibration and the C(alpha)H bending vibration to the amide backbone conformation. We demonstrate that this sensitivity results from a Ramachandran dihedral psi angle dependent coupling of the amide N-H motion to (C)C(alpha)H motion, which results in a psi dependent mixing of the Am III and the (C)C(alpha)H bending motions. The vibrations are intimately mixed at psi approximately 120 degrees, which is associated with both the beta-sheet conformation and random coil conformations. In contrast, these motions are essentially unmixed for the alpha-helix conformation where psi approximately -60 degrees. Theoretical calculations demonstrate a sinusoidal dependence of this mixing on the psi angle and a linear dependence on the distance separating the N-H and (C)C(alpha)H hydrogens. Our results explain the Am III frequency dependence on conformation as well as the resonance Raman enhancement mechanism for the (C)C(alpha)H bending UV Raman band. These results may in the future help us extract amide psi angles from measured UV resonance Raman spectra.     

A conformational dynamics study of alpha-l-Rhap-(1-->2)[alpha-l-Rhap-(1-->3)]-alpha-l-Rhap-OMe in solution by NMR experiments and molecular simulations

The conformational preference of alpha-l-Rhap-(1-->2)[alpha-l-Rhap-(1-->3)]-alpha-l-Rhap-OMe in solution has been studied by NMR spectroscopy using one-dimensional (1)H,(1)H T-ROESY experiments and measurement of trans-glycosidic (3)J(C,H) coupling constants. Molecular dynamics (MD) simulations with a CHARMM22 type of force field modified for carbohydrates were performed with water as the explicit solvent. The homonuclear cross-relaxation rates, interpreted as effective proton-proton distances, were compared to those obtained from simulation. Via a Karplus torsional relationship, (3)J(C,H) values were calculated from simulation and compared to experimental data. Good agreement was observed between experimental data and the MD simulation, except for one inter-residue T-ROE between protons in the terminal sugar residues. The results show that the trisaccharide exhibits substantial conformational flexibility, in particular along the psi glycosidic torsion angles. Notably, for these torsions, a high degree of correlation (77%) was observed in the MD simulation revealing either psi(2)(+) psi(3)(+) or psi(2)(-)psi(3)(-) states. The simulations also showed that non-exoanomeric conformations were present at the phi torsion angles, but to a limited extent, with the phi(3) state populated to a larger extent than the phi(2) state. Further NMR analysis of the trisaccharide by translational diffusion measurements and (13)C T(1) relaxation experiments quantified global reorientation using an anisotropic model together with interpretation of the internal dynamics via the "model-free" approach. Fitting of the dynamically averaged states to experimental data showed that the psi(2)(+)psi(3)(+) state is present to approximately 49%, psi(2)(-) psi(3)(-) to approximately 39%, and phi(3) (non-exo) to approximately 12%. Finally, using a dynamic and population-averaged model, (1)H,(1)H T-ROE buildup curves were calculated using a full relaxation matrix approach and were found to be in excellent agreement with experimental data, in particular for the above inter-residue proton-proton interaction between the terminal residues.     

Estimating kinetic rates from accelerated molecular dynamics simulations: alanine dipeptide in explicit solvent as a case study

Molecular dynamics (MD) simulation is the standard computational technique used to obtain information on the time evolution of the conformations of proteins and many other molecular systems. However, for most biological systems of interest, the time scale for slow conformational transitions is still inaccessible to standard MD simulations. Several sampling methods have been proposed to address this issue, including the accelerated molecular dynamics method. In this work, we study the extent of sampling of the phi/psi space of alanine dipeptide in explicit water using accelerated molecular dynamics and present a framework to recover the correct kinetic rate constant for the helix to beta-strand transition. We show that the accelerated MD can drastically enhance the sampling of the phi/psi conformational phase space when compared to normal MD. In addition, the free energy density plots of the phi/psi space show that all minima regions are accurately sampled and the canonical distribution is recovered. Moreover, the kinetic rate constant for the helix to beta-strand transition is accurately estimated from these simulations by relating the diffusion coefficient to the local energetic roughness of the energy landscape. Surprisingly, even for such a low barrier transition, it is difficult to obtain enough transitions to accurately estimate the rate constant when one uses normal MD.     

Structure distribution in an elastin-mimetic peptide (VPGVG)3 investigated by solid-state NMR

Elastin is an extracellular-matrix protein that imparts elasticity to tissues. We have used solid-state NMR to determine a number of distances and torsion angles in an elastin-mimetic peptide, (VPGVG)3, to understand the structural basis of elasticity. C-H and C-N distances between the V6 carbonyl and the V9 amide segment were measured using 13C-15N and 13C-1H rotational-echo double-resonance experiments. The results indicate the coexistence of two types of intramolecular distances: a third of the molecules have short C-H and C-N distances of 3.3 +/- 0.2 and 4.3 +/- 0.2 A, respectively, while the rest have longer distances of about 7 A. Complementing the distance constraints, we measured the (phi, psi ) torsion angles of the central pentameric unit using dipolar correlation NMR. The -angles of P7 and G8 are predominantly ~150, thus restricting the majority of the peptide to be extended. Combining all torsion angles measured for the five residues, the G8 C chemical shift, and the V6-V9 distances, we obtained a bimodal structure distribution for the PG residues in VPGVG. The minor form is a compact structure with a V6-V9 C=O-HN hydrogen bond and can be either a type II -turn or a previously unidentified turn with Pro (phi = -70, psi= 20 +/- 20) and Gly ( phi= -100 +/- 20, psi = -20 +/- 20). The major form is an extended and distorted beta-strand without a V6-V9 hydrogen bond and differs from the ideal parallel and antiparallel beta-strands. The other three residues in the VPGVG unit mainly adopt antiparallel beta-sheet torsion angles. Since (VPGVG)3 has the same 13C and 15N isotropic and anisotropic chemical shifts as the elastin-mimetic protein (VPGXG)n (X = V and K, n = 195), the observed conformational distribution around Pro and Gly sheds light on the molecular mechanism of elastin elasticity.     

Tripeptides adopt stable structures in water. A combined polarized visible Raman,FTIR, and VCD spectroscopy study

We have measured the band profile of amide I in the infrared, isotropic, and anisotropic Raman spectra of L-alanyl-D-alanyl-L-alanine, acetyl-L-alanyl-L-alanine, L-vanyl-L-vanyl-L-valine, L-seryl-L-seryl-L-serine, and L-lysyl-L-lysyl-L-lysine at acid, neutral, and alkaline pD. The respective intensity ratios of the two amide I bands depend on the excitonic coupling between the amide I modes of the peptide group. These intensity ratios were obtained from a self-consistent spectral decomposition and then were used to determine the dihedral angles between the two peptide groups by means of a recently developed algorithm (Schweitzer-Stenner, R. Biophys. J. 2002, 83, 523-532). The validity of the obtained structures were checked by measuring and analyzing the vibrational circular dichroism of the two amide I bands. Thus, we found two solutions for all protonation states of trialanine. Assuming a single conformer, one obtains a very extended beta-helix-like structure. Alternatively, the data can be explained by the coexistence of a 3(1)(PII) and a beta-sheet-like structure. Acetyl-L-alanyl-L-alanine exhibits a structure which is very similar to that obtained for trialanine. The tripeptide with the central D-alanine adopts an extended structure with a negative psi and a positive phi angle. Trivaline and triserine adopt single beta(2)-like structures such as that identified in the energy landscape of the alanine dipeptide. Trilysine appears different from the other investigated homopeptides in that it adopts a left-handed helix which at acid pD is in part stabilized by hydrogen bonding between the protonated carboxylate (donor) and the N-terminal peptide carbonyl. Our result provides compelling evidence for the capability of short peptides to adopt stable structures in an aqueous solution, which at least to some extent reflect the intrinsic structural propensity of the respective amino acids in proteins. Furthermore, this paper convincingly demonstrates that the combination of different vibrational spectroscopies provides a powerful tool for the determination of the secondary structure of peptides in solution.     

Toward direct determination of conformations of protein building units from multidimensional NMR experiments part II: a theoretical case study of formyl-L-valine amide

Chemical shielding anisotropy tensors have been determined for all twenty-seven characteristic conformers of For-L-Val-NH2 using the GIAO-RHF formalism with the 6-31 + G* and TZ2P basis sets. The individual chemical shifts and their conformational averages have been compared to their experimental counterparts taken from the BioMagnetic Resonance Bank (BMRB). At the highest level of theory applied, for all nuclei but the amide proton, deviations between statistically averaged theoretical and experimental chemical shifts are as low as 1-3%. Correlated chemical shift plots of selected nuclei, as function of the respective phi, psi, chi1, and chi2 torsional angles, have been generated. On two-dimensional chemical shift-chemical shift plots, for example, 1H(NH)-15N(NH) and 15N(NH)-13Calpha, regions corresponding to major conformational clusters have been identified, providing a basis for the quantitative identification of conformers from NMR shift data. Experimental NMR resonances of nuclei of valine residues have been deduced from 18 selected proteins, resulting in 93 1Halpha-13Calpha chemical shift pairs. These experimental results have been compared to relevant ab initio values revealing remarkable correlation between the two sets of data. Correlations of 1Halpha and 13Calpha values with backbone conformational parameters (phi and psi) have also been found for all pairs (e.g. 1Halpha/phi and 13Calpha/phi) but 1Halpha/psi. Overall, the appealing idea of establishing backbone folding of proteins by employing chemical shift information alone, obtained from selected multiple-pulse NMR experiments (e.g. 2D-HSQC, 2D-HMQC, and 3D-HNCA), has received further support.     

The conformation of tetraalanine in water determined by polarized Raman, FT-IR, and VCD spectroscopy

The present article reports the conformation of cationic tetraalanine in aqueous solution. The determination of the dihedral angles of the two central amino acid residues was achieved by analyzing the amide I' band profile in the respective polarized visible Raman, Fourier transform-IR, and vibrational circular dichroism (VCD) spectra by means of a novel algorithm which utilizes the excitonic coupling between the amide I modes of nearest neighbor and second nearest peptide groups. It is an extension of a recently developed theory (Schweitzer-Stenner, R. Biophys. J., 2002, 83, 523-532). UV electronic circular dichroism (ECD) spectra of the peptides were used to validate the results of the structure analysis. The analyses yielded the dihedral angles (phi(12), psi(12)) = (-70 degrees, 155 degrees ) and (phi(23), psi(23)) = (-80 degrees, 145 degrees ). The obtained values are very close to the Ramachandran coordinates of the polyproline II helix (PPII). The data suggest that this is the conformation predominantly adopted by the peptide at room temperature. This notion was corroborated by the corresponding electronic circular dichroism spectrum. Tetraalanine exhibits a higher propensity for PPII than trialanine for which a 50:50 mixture of polyproline II and an extended beta-strand-like conformation was obtained from recent spectroscopic studies (Eker et al., J. Am. Chem. Soc. 2002, 124, 14330-14341). The temperature dependence of the CD spectra rule out that any cooperativity is involved in the strand if PPII transition. This led to the conclusion that solvent-peptide interactions give rise to the observed PPII stability. Our result can be utilized to understand why the denaturation of helix-forming peptides generally yields a PPII rather than a heterogeneous random conformation.     

Flexibility of "polyunsaturated fatty acid chains" and peptide backbones: A comparative ab initio study

The conformational properties of omega-3 type of polyunsaturated fatty acid (PUFA) chains and their fragments were studied using Hartree-Fock (RHF/3-21G) and DFT (B3LYP/6-31G(d)) methods. Comparisons between a unit (U) fragment of the PUFA chain and a mono N-Ac-glycine-NHMe residue show that both structures have the same sequence of sp2-sp3-sp2 atoms. The flexibility of PUFA originates in the internal rotation about the above pairs of sigma bonds. Therefore, potential energy surfaces (PESs) were generated by a scan around the terminal dihedral angles (phi t1 and phi t2) as well as the phi 1 and psi 1 dihedrals of both 1U congeners (Me-CHCH-CH2-CHCHMe and MeCONH-CH2-CONHMe) at the RHF/3-21G level of theory. An interesting similarity was found in the flexibility between the cis allylic structure and the trans peptide models. A flat landscape can be seen in the cis 1U (hepta-2,5-diene) surface, implying that several conformations are expected to be found in this (PES). An exhaustive search carried out on the 1U and 2U models revealed that straight chain structures such as trans and cis beta (phi 1 approximately psi 1 approximately 120 degrees; phi 2 approximately psi 2 approximately -120 degrees) or trans and cis extended (phi 1 approximately psi 1 approximately phi 2 approximately psi 2 approximately 120 degrees) can be formed at the lowest energy of both isomers. However, forming helical structures, such as trans helix (phi 1 approximately -120 degrees, psi 1 approximately 12 degrees; phi 2 approximately -120 degrees, psi 2 approximately 12 degrees) or cis helix (phi 1 approximately -130 degrees, psi 1 approximately 90 degrees; phi 2 approximately -145 degrees, psi 2 approximately 90 degrees) will require more energy. These six conformations, found in 2U, were selected to construct longer chains such as 3U, 4U, 5U, and 6U to obtain the thermochemistry of secondary structures. The variation in the extension or compression of the chain length turned out to be a factor of 2 between the helical and nonhelical structures. The inside diameter of the "tube" of cis helix turned out to be 3.5 A after discounting the internal H atoms. Thermodynamic functions were computed at the B3LYP/6-311+G(2d,p)//B3LYP/6-31G(d). The cis-trans isomerization energy of 1.7 +/- 0.2 kcal mol(-1) unit(-1) for all structure pairs indicates that the conformer selection was consistent. A folding energy of 0.5 +/- 0.1 kcal mol(-1) unit(-1) has been extracted from the energy comparison of the helices and most extended nonhelical structures. The entropy change associated with the folding (Delta S(folding)) is decreases faster with the degree of polymerization (n) for the cis than for the trans isomer. As a consequence, the linear relationships between (Delta G(folding)) and n for the cis and trans isomer crossed at about n = 3. This suggested that the naturally occurring cis isomer less ready to fold than the trans isomer since a greater degree of organization is exhibited by the cis isomer during the folding process. The result of this work leads to the question within the group additivity rule: could the method applied in our study of the folding of polyallylic hydrocarbons be useful in investigating the thermochemistry of protein folding?     

Single-conformation infrared spectra of model peptides in the amide I and amide II regions: Experiment-based determination of local mode frequencies and inter-mode coupling

Single-conformation infrared spectra in the amide I and amide II regions have been recorded for a total of 34 conformations of three α-peptides, three β-peptides, four α∕β-peptides, and one γ-peptide using resonant ion-dip infrared spectroscopy of the jet-cooled, isolated molecules. Assignments based on the amide NH stretch region were in hand, with the amide I∕II data providing additional evidence in favor of the assignments. A set of 21 conformations that represent the full range of H-bonded structures were chosen to characterize the conformational dependence of the vibrational frequencies and infrared intensities of the local amide I and amide II modes and their amide I∕I and amide II∕II coupling constants. Scaled, harmonic calculations at the DFT M05-2X∕6-31+G(d) level of theory accurately reproduce the experimental frequencies and infrared intensities in both the amide I and amide II regions. In the amide I region, Hessian reconstruction was used to extract local mode frequencies and amide I∕I coupling constants for each conformation. These local amide I frequencies are in excellent agreement with those predicted by DFT calculations on the corresponding (13)C = (18)O isotopologues. In the amide II region, potential energy distribution analysis was combined with the Hessian reconstruction scheme to extract local amide II frequencies and amide II∕II coupling constants. The agreement between these local amide II frequencies and those obtained from DFT calculations on the N-D isotopologues is slightly worse than for the corresponding comparison in the amide I region. The local mode frequencies in both regions are dictated by a combination of the direct H-bonding environment and indirect, "backside" H-bonds to the same amide group. More importantly, the sign and magnitude of the inter-amide coupling constants in both the amide I and amide II regions is shown to be characteristic of the size of the H-bonded ring linking the two amide groups. These amide I∕I and amide II∕II coupling constants remain similar in size for α-, β-, and γ-peptides despite the increasing number of C-C bonds separating the amide groups. These findings provide a simple, unifying picture for future attempts to base the calculation of both nearest-neighbor and next-nearest-neighbor coupling constants on a joint footing.     

Uncoupled peptide bond vibrations in alpha-helical and polyproline II conformations of polyalanine peptides

We examined the 204-nm UV resonance Raman (UVR) spectra of the polyproline II (PPII) and alpha-helical states of a 21-residue mainly alanine peptide (AP) in different H2O/D2O mixtures. Our hypothesis is that if the amide backbone vibrations are coupled, then partial deuteration of the amide N will perturb the amide frequencies and Raman cross sections since the coupling will be interrupted; the spectra of the partially deuterated derivatives will not simply be the sum of the fully protonated and deuterated peptides. We find that the UVR spectra of the AmIII and AmII' bands of both the PPII conformation and the alpha-helical conformation (and also the PPII AmI, AmI', and AmII bands) can be exactly modeled as the linear sum of the fully N-H protonated and N-D deuterated peptides. Negligible coupling occurs for these vibrations between adjacent peptide bonds. Thus, we conclude that these peptide bond Raman bands can be considered as being independently Raman scattered by the individual peptide bonds. This dramatically simplifies the use of these vibrational bands in IR and Raman studies of peptide and protein structure. In contrast, the AmI and AmI' bands of the alpha-helical conformation cannot be well modeled as a linear sum of the fully N-H protonated and N-D deuterated derivatives. These bands show evidence of coupling between adjacent peptide bond vibrations. Care must be taken in utilizing the AmI and AmI' bands for monitoring alpha-helical conformations since these bands are likely to change as the alpha-helical length changes and the backbone conformation is perturbed.     

Glucose orientation and dynamics in alpha-, beta-, and gamma-cyclodextrins

We investigate, using molecular dynamics (MD) computer simulations, the conformational behavior of alpha-, beta-, and gamma-cyclodextrins (CDs). Our analysis of a 30 ns trajectory of CD solution dynamics reveals the underlying conformational behaviours of the CDs that explain their relative flexibility. The distributions of the torsion angles related to the glycosidic linkages, P(phi,psi) were calculated for the three CDs. Most noticeable is the limited range in phi torsion rotations compared with psi rotations for all the CDs. This difference between the three CDs is amplified in the motion and dynamics of their glucose monomers when we monitor their orientational and librational positions relative to the macrocyclic mean plane. The relaxation times of the monomers to their equilibrium orientations follow the pattern gamma-CD > alpha-CD > beta-CD. The root-mean-square deviations of the motion of the monomer centers of mass from the mean macrocyclic planes exhibit the same trend.